The invention relates to fuel injection pumps for internal combustion engines. More particularly, the invention relates to a fuel injection pump in which a piston supplies fuel under pressure to the several combustion chambers of the engine. The fuel injection pump includes a movable member which determines the amount of fuel delivered to the engine and the pump includes a sump or low pressure chamber which is coupled to the high pressure or working chamber via a throttled conduit. In a known fuel injection pump of this type, the suction channel leading from the sump to the pressure chamber has a variable throttle whose active cross section determines the amount of fuel which is aspirated by the engine during the suction stroke of the piston and which thus is finally injected. A storage chamber of constant or variable volume is coupled to the pressure chamber via a second variable throttle. However, in this known fuel injection pump, the first variable throttle in the suction channel substantially alone determines the amount of injected fuel, whereas the second throttle in the passage between the pressure chamber and the storage chamber permits only small amounts of fuel to be drained during the delivery stroke of the piston. Therefore, the injected quantity as controlled by a regulator can be adapted to only a number of selected operational states of the engine to which the injection pump is fitted. Furthermore, the change of the effective throttle cross section of the second throttle in this known pump is invariably related to load conditions and engine speed.